A key prediction of many inflationary cosmological scenarios is that the region of space visible to any single observer is a tiny fraction of the total volume of spacetime. Moreover, it is possible (and perhaps likely) that the event we characterise as the Big Bang is not unique, so that there are many separate universes which only interact with one another (if they do so at all) in very rare conditions. 

This leads to speculation that our universe is embedded in a larger multiverse. Consequently, we can find ourselves in the paradoxical position of being able to describe these multiverse proposals using the tools of mathematical cosmology even thought their consequences are unobservable, even in principle.  

Different cosmological theories predict different multiverse scenarios. Consequently, understanding differences allows quantitative discussions of multiverse proposals. This line of thought is an ongoing interest of Easther and the Auckland group.

In particular, string theory suggests the existence of a “landscape” – several hundred degrees of freedom that are connected by a complicated potential function.  Locations in the landscape where all directions are “uphill” are (local) minima and each minimum corresponds to a possible configuration of the “laws” of particle physics. The landscape may contain 10⁵⁰⁰ such minima. In principle the properties of the landscape are computable but in practice it may be intractably difficult to do so. 

However, many of the properties of the landscape follow purely from its complexity and high dimensionality. Consequently, Easther has been looking at the properties of simple random functions in many dimensions. Their generic properties can be computed and we use these as a proxy for the full landscape. 

[Research content below.]